The gain dynamics of a semiconductor optical amplifier (SOA) were measured using pump-probe techniques for the amplification of 750 fs pulses, 6.5 ps pulses and multiwavelength pulses, obtained from an external cavity semiconductor mode-locked laser. Furthermore, the intracavity gain dynamics of an external cavity semiconductor mode-locked laser was measured under multiwavelength operation. The experimental results show how the inherent chirp in pulses from external cavity semiconductor mode-locked lasers result in a slow gain depletion without significant fast gain dynamics. This mitigates gain competition between wavelength channels and nonlinearities in the gain media (SOA), enabling the multiwavelength operation of external cavity semiconductor mode-locked lasers. Numerical simulations support the experimental results.